Preheat oven to 400 degrees. If using fresh broccoli, steam in a microwave-safe dish by adding a few tablespoons water, covering with a lid, and microwaving 2-4 minutes until bright green and crisp-tender. If using frozen, thaw and squeeze out as much liquid as possible. Place steamed or thawed broccoli in the bowl of a food processor and pulse until finely chopped (but not pureed).

Assemble lasagna: in an 8-inch square baking dish, spoon a thin layer of sauce. Top with two noodles, a quarter of remaining sauce, and a third of the broccoli mixture. Repeat twice. Top with the remaining two noodles and sauce. Sprinkle the top with remaining 1/4 c. mozzarella and 2 Tbsp. Parmesan.